Level-crossing time interval estimation techniques can be useful for signal frequency estimation, rotation angular velocity estimation and signal modulation classification. The time interval between two level-crossing points of a periodic function can be estimated by using a moving average of the level-crossing time samples. Current level-crossing time interval estimation techniques are based on a certain number of important mathematical expressions.
Assuming that the signal g(x) is periodic in a given time domain xL≦x≦xR and also assume that signal g(x) has N number of level-crossing time samples, or measurements, x(k), x(k−1), . . . , x(k−N+1) between xL and xR such that g[x(k)]=g[x(k−1)]= . . . =g[x(k−N+1)]=E, where E is a given level for measuring crossings. If E=0, the time samples x(k), x(k−1), . . . , X(k−N+1) are considered to be zero-crossing points. The time interval between two level-crossing time samples, x(k) and x(k−v), is then defined as v-step differential level-crossing time-interval, denoted by the expression:y(k,v)=x(k)−x(k−v),  (1)where 1≦vV≦N−1 . . . is a positive integer. Since the function g(x) is noisy in practice, the level-crossing time interval will be estimated by taking the time average of:y(k,1)=x(k)−x(k−1)  (2)as shown below,
                              m          ⁡                      (                          k              ,                              N                -                1                                      )                          =                              1                          N              -              1                                ⁢                                    ∑                              j                =                0                                            N                -                2                                      ⁢                                                  ⁢                          y              ⁡                              (                                                      k                    -                    j                                    ,                  1                                )                                                                        (        3        )            Substituting Equation 2 into equation 3, the level-crossing time interval estimation is:
                              m          ⁡                      (                          k              ,                              N                -                1                                      )                          =                                                            x                ⁡                                  (                  k                  )                                            -                              x                ⁡                                  (                                      k                    -                    N                    +                    1                                    )                                                                    N              -              1                                =                                    1                              N                -                1                                      ⁢                          y              ⁡                              (                                  k                  ,                                      N                    -                    1                                                  )                                                                        (        4        )            For N given time samples, x(k), x(k−1), . . . , x(k−N+1), the estimation in Equation 4 uses only the first and the last samples, x(k−N+1) and x(k), and all other time samples x(k−1), x(k−2), . . . , x(k−N+2) are not counted. Therefore, the current estimation technique is based on only two samples so that the information in all other N−2 time samples is not utilized. This is known as two-sample estimation.
There are a number of disadvantages, shortcomings and limitations with the current two-sample estimation technique. One problem with the current two-sample estimation technique is that it only uses two samples at a time, so that the information from numerous other given time samples is not accessed and used. Another problem with the current two-sample estimation technique is that noises in samples x(k−N+1) and x(k) from various sources, such as electronic components, interference in transmission or even thermal noise, will directly affect the two-sample estimation result of m(k,N−1). Thus, there has been a long-felt need for other estimating techniques and devices that are quieter and extract more information from given time samples than the current two-sample approach.
The long-felt need for new time estimation techniques has now been answered with N-sample level-crossing estimator methods and devices that extract more information from given time samples than the current two-sample approach and that are more resistant to interference from noises. The two-mean level-crossing time-interval and signal frequency estimation method of the present invention extracts more information from given time samples than existing methods, can advantageously estimate a level-crossing time interval with a limited number of time samples and is more accurate than the inefficient and noisy prior art estimation techniques. The present invention also encompasses addition only one-step differential level-crossing time-interval estimator and one-step differential level-crossing time-interval estimator devices that are less noisy than inefficient prior art estimation techniques.